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One‐dimensional q ‐Dirac equation
Author(s) -
Allahverdiev Bilender P.,
Tuna Hüseyin
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4529
Subject(s) - mathematics , eigenfunction , orthonormal basis , eigenvalues and eigenvectors , orthogonality , uniqueness , mathematical analysis , dirac equation , countable set , function (biology) , pure mathematics , mathematical physics , quantum mechanics , geometry , physics , evolutionary biology , biology
In this paper, we introduce a q ‐analog of 1‐dimensional Dirac equation. We investigate the existence and uniqueness of the solution of this equation. Later, we discuss some spectral properties of the problem, such as formally self‐adjointness, the case that the eigenvalues are real, orthogonality of eigenfunctions, Green function, existence of a countable sequence of eigenvalues, and eigenfunctions forming an orthonormal basis ofL q 2 ( 0 , a ; E ) . Finally, we give some examples.